Circle has a mental image of, well, a circle. Hence, a sewing circle conjures an image of people sitting in a circle, sewing. That would be hard to imagine with tennis. A sewing club might be a group of on-line people who chat about sewing, but a sewing circle would certainly imply that they sat together. A club also implies some form of official membership. One is a "member" of a club, even if it is very informal. A "circle" may be a simple open invitation. You just go, sit with the others, and sew. A "club" would have a bit more structure, might even have a president or a regular meeting day and someone who takes down the minutes. A circle probably would not have this structure.
A tennis club or golf club is usually a very formal structure, with rules of order and membership requirements and dues.
As for what to call such an assembly dedicated to making dessert(s), it would depend on how it's organized. It might be a dessert class, a dessert club, a dessert group - but I've never really thought of it as a dessert circle, because there has to be someone at the helm, teaching, even if it's a different teacher/demonstrator every few minutes. A circle has no head, no top.
Now, as for the dessert(s) question. Both are correct. To say you like to make desserts suggests you have a range of different sweet options you enjoy preparing. If you say, I like to make dessert, it may mean that you always bring the same cherry cheesecake to every function. On the other hand, it may mean exactly the same thing as desserts.